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HW due 1/24 – begin on pg 612 1, 11, 13, 14, 17, 21, 24, 25, 35, 37, 49, 56 (look at problem 20 below), 61
Probability & Odds
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1. In a probability space, which of the following statements is not true?
A) All outcomes are equally likely.
B) The probability of the sample space is always equal to 1.
C) The impossible event always has probability equal to 0.
D) All probabilities are between 0 and 1 (0 and 1 included).
E) All of these statements are true.
2.
Consider the sample space S = {o1, o2, o3, o4, o5 }.
Suppose you are given Pr(o1) = 0.25 and Pr( o2 ) = 0.15. Find the
probability assignment for the probability space when o3, o4, all have the o5 same probability.
A) Pr(o1) = 0.25, Pr(o2) = 0.15, Pr(o3) = 0.15, Pr(o4) = 0.15, Pr(o5) = 0.15
B) Pr(o1) = 0.25, Pr(o2) = 0.15, Pr(o3) = 0.2, Pr(o4) = 0.2, Pr(o5) = 0.2
C) Pr(o1) = 0.25, Pr(o2) = 0.15, Pr(o3) = 0.3, Pr(o4) = 0.15, Pr(o5) = 0.15
D) Pr(o1) = 0.2, Pr(o2) = 0.2, Pr(o3) = 0.2, Pr(o4) = 0.2, Pr(o5) = 0.2
E) Pr(o1) = 0.25, Pr(o2) = 0.15, Pr(o3) = 0.15, Pr(o4) = 0.3, Pr(o5) = 0.15
3.
Five horses (A, B, C, D, and E) are racing at the local track. According to the oddsmakers, A has a "one in four"
probability of winning [i.e. Pr(A) = ¼ ], B has a "one in ten" probability of winning, and C has a "one in twenty"
probability of winning. The remaining two horses both have the same probability of winning. Find the probability
assignment for the probability space.
A) Pr(A) = 1/4, Pr(B) = 1/10, Pr(C) = 1/20, Pr(D) = 3/40, Pr(E) = 3/40
B) Pr(A) = 1/4, Pr(B) = 1/10, Pr(C) = 1/20, Pr(D) = 3/20, Pr(E) = 7/20
C) Pr(A) = 1/4, Pr(B) = 1/10, Pr(C) = 1/20, Pr(D) = 1/20, Pr(E) = 1/20
D) Pr(A) = 1/4, Pr(B) =1/10, Pr(C) = 1/20, Pr(D) = 3/20, Pr(E) = 3/20
E) Pr(A) = 1/4, Pr(B) = 1/10, Pr(C) =1/20, Pr(D) = 3/10, Pr(E) = 3/10
4.
In the spinner shown below, the regions numbered 1 and 2 correspond to 90° angles. The region numbered 3
corresponds to a 100° angle and the region numbered 4 corresponds to a 60° angle. Find the probability that,
when spun randomly, the spinner will land on the region numbered 5.
A) 1/9
B) 1/18
C) 1/16
D)1/17
E) none of these
1
Four basketball teams called A, B, C, and D are entered in a tournament. According to the odds makers, the probability
that team A will win the tournament is Pr(A) = 0.1, and the other three teams all have an equal probability of winning the
tournament.
5. What is the probability that team A will not win the tournament?
A) 0.4
B) 0.3
C) 0.9
D) cannot be determined from the information given
E) none of these
6.
What is the probability that team D will win the tournament?
A) 0.25
B) 0.9
C) 0.3
D) 0.45
E) none of these
Solve the problem.
7. A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by E:
"both dice will come up as even numbers" is
A) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4),
6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
B) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}.
C) {(1, 1), (2, 2), (2, 4), (2, 6), (3, 3), (4, 2), (4, 4), (4, 6), (5, 5), (6, 2), (6, 4), (6, 6)}.
D) {(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)}.
E) none of these
8.
(4,
A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by E:
"at least one die will come up as an even number" is
A) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6),
4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}.
(5,
B) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4),
6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
C) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}.
(4,
D) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1),
5)}.
E) none of these
(6,
2
A pair of honest dice is rolled, and the number on each die is noted.
9. What is the probability of rolling a total of 2?
A) 1/6
B) 1/18
C) 1/3
D) 1/36
E) none of these
10. What is the probability of rolling a total of 7?
A) 1/36
B) 7/36
C) 1/3
D) 1/6
E) none of these
11. What is the probability of rolling a total of 11?
A) 1/36
B) 1/6
C) 1/4
D) 1/18
E) none of these
12. What is the probability of rolling a total of either 7 or 11?
A) 1/6
B) 1/4
C) 1/36
D) 1/18
E) none of these
13. What is the probability of rolling a total that is neither 7 nor 11?
A) 7/9
B) 17/18
C) 5/6
D) 1/2
E) none of these
Four drivers called A, B, C, and D are entered in a race. According to the odds makers, the probability that the driver A
will win the race is Pr(A) = 0.4, and the other three drivers all have an equal probability of winning the race.
14. What is the probability that the driver B will not win the race?
A) 0.6
B) 0.4
C) 0.8
D) cannot be determined from the information given
E) none of these
Solve the problem.
15. If a fair coin is tossed twice, the probability that both tosses will come up heads is
A) 3/4
B) 1/2
C) 1/4
D) 1/3
E) none of these
3
16. If a fair coin is tossed twice, the probability that at least one of the tosses will come up heads is
A) 1/3
B) 1/4
C) 1/2
D) 3/4
E) none of these
17. If a fair coin is tossed twice, the probability of both tosses coming up the same is
A) 1/2
B) 1/4
C) 3/4
D) 1/3
E) none of these
18. If a fair coin is tossed three times, the probability of tossing three heads is
A) 3/8
B) 1/8
C) 1/4
D) 1/2
E) none of these
19. An honest coin is tossed ten times. The probability of tossing one head and nine tails is
A) 1/9
B) 1/1024
C) 5/512
D) 1/10
E) none of these
20. An honest coin is tossed ten times.
A) 1/5
B) 5/512
C) 45/1024
D) 1/512
E) none of these
The probability of tossing two heads and eight tails is
21. An honest coin is tossed ten times. The probability that the number of heads is double the number of tails is
A) 1/2
B) 1/3
C) 2/3
D) 0.
E) none of these
22. An honest coin is tossed ten times.
A) 2/3
B) 1/2
C) 0
D) 1/3
E) none of these
The probability that the number of heads is triple the number of tails is
23. Suppose that an honest coin is tossed ten times. What is the probability that it will come up heads at least once?
A) 9/10
B) 10/9
C) 1023/1024
D) 1/2
E) none of these
4
24. Suppose that an honest coin is tossed ten times.
A) 1/512
B) 1013/1024
C) 507/512
D) 4/5
E) none of these
What is the probability that at least twice it comes up heads?
25. If the chances of rain tomorrow are 20%, then the odds of rain tomorrow can be given as
A) 2 to 8.
B) 2 to 10.
C) 2 to 1.
D) 2 to 12.
E) none of these
26. If the probability of snow on Tuesday is 0.125, then the odds of snow on Tuesday can be given as
A) 1 to 8.
B) 1 to 7.
C) 1 to 12.5.
D) 125 to 1.
E) none of these
Four drivers called A, B, C, and D are entered in a race. According to the odds makers, the probability that the driver A
will win the race is Pr(A) = 0.4, and the other three drivers all have an equal probability of winning the race.
27. What are the odds that driver D will win the race?
A) 1 to 6
B) 1 to 4
C) 1 to 3
D) 4 to 6
E) none of these
Solve the problem.
28. Suppose that the odds of winning the grand prize in a raffle are 1 to 7.
prize?
A) 1/7
B) 1/8
C) 1/6
D) 6/7
E) none of these
What is the probability of winning the grand
29. Suppose that the odds of winning the grand prize in a raffle are 1 to 15. What is the probability of winning the grand
prize?
A) 1/15
B) 14/15
C) 1/14
D) 1/16
E) none of these
30. Suppose that the odds against winning the grand prize in the lottery are 80,000,000 to 1.
winning the lottery?
A) 79.999,999/80,000,000
B) 1/80,000,000
C) 1/79,999,999
D) 1/80,000,001
E) none of these
What is the probability of
5
1) A
2) B
3) E
4) B
5) C
6) C
7) B
8) B
9) D
10) D
11) D
12) E
13) A
14) C
15) C
16) D
17) A
18) B
19) C
20) C
21) D
22) C
23) C
24) B
25) A
26) B
27) B
28) B
29) D
30) D
6